The Colossus of Rhodes * Epius and Phemius * The Delian Puzzle * Square–Cube Law * Size Does Matter * The Apple’s Descent * Isaac Newton * The Heat Seekers * Form and Function * Life on Earth * The Tree Warriors

     Leonardo’s Polyhedrons * Luca Pacioli and Johannes Kepler * The Ladder of Dimensions * Other Dimensional Cubes * Salvador Dali and the Fourth Dimension * A Natural Five * The Perfect Die * Pascal’s Triangle * Cardano * William Blake’s Dice

    Chaos Theory * The Pendulum * Chaos on a Calculator * Nature’s Patterns * The Logistic Function * One, Two, Four, … Chaos * Chaos on a Personal Computer * Bifurcation Diagrams * The Butterfly Effect * The Lorenz Attractor * The Rider in the Whirlwind * Contingent History * Ab–Surd Universe * Root Fractals * Long Night’s Journey into Light

The Koch Snowflake * Benoit Mandelbrot * Fractal Dimensions * The Sierpinski Triangle * Self Similarity * The Chaos Game * The Odd and Even Triangle * The Garden of Simple Complexity  * Julia Sets * The Mandelbrot Set * Seahorse Canyon * Departure

The Genesis of Numbers * The Sign of the Fish * 153 Fishes in the Net * Triangle Numbers * Fish Fry * Invention or Discovery * Numerical Miracles in the Koran * Michael Drosnin and Equidistant Letter Sequences * The Number Seven in Our Culture

Pi (p) and Curves of Constant Width * Meandering Streams and Pi * Biblical Value of Pi * Circle Squarers * Classification of Numbers * Continued Fractions and Pi * The Field of Dreams * Fibonacci Numbers * Phi (j) — the Golden Number * Sunflower Spirals * Van Gogh’s Sunflowers * Numbers: Cultural * The Pyramid of Giza * Phi in the Parthenon * Adam’s Bellybutton * Vitruvian Man * Phi in Art * Phi Foolishness * The Truth about The Da Vinci Codes * The Texture of Infinity * Delta (d) — the Feigenbaum Constant * Paleolithic Cave Art

Animal Double Printing * Archimedes’ Tombstone * Bouncing Balls and Photons * Night Vision * The Cowboy’s Dilemmas * Starry Night * Queen Dido’s Puzzle * The Least–Action Principle * The Skin on Water and Air * Soap Bubbles * Minimum Paths * The Argument from Design * Minimal Surfaces * Cubical Soap Bubbles * The Air Pressure Paradox * Geometry of Soap Bubbles and Films * The Dance of Life * The Fox Knows Many Things

Symmetry and Beauty * Planes of Symmetry * Handedness in Nature * Reflections of Einstein’s Face * Inverted Drawings * Whom the Gods Love * Symmetry Groups * Platonic Solids * The Alhambra * The Seven Frieze Patterns * Broken Symmetry * Instability — the Creator * Art and Symmetry * Nature and Symmetry Breaking * Cosmic Fingerprint

Join the Dots * Spirals in Nature and Art * Explosions in Nature * The Geometry of Spirals, Meanders, and Explosions * The Lady and the Ermine * Truth in Nature, Art, and Mathematics * False Patterns * The Cluster Illusion * The Birthday Puzzle * The Hot Hand * The Riders * The Game of Life * Emergent Properties * How the Zebra Gets its Stripes

Epius and Phemius * The Greeks and Deduction * The Renaissance and Induction * Art and Science * Creativity in Science * Is Seeing Believing? * Illusions * The Lords of the Rings * The Deception Room * Pascal’s Triangle Upside Down * Knowledge or Certainty * Epius and Phemius * The True Immortals